As someone who suffers with depression, I can tell you that it is not unusual for it to take several weeks for the medication to help. It did for me.
Hang in there. I know it's hard on everyone when a family member suffers from depression. It will get better, but it can sometimes take a while and sometimes requires changing medications. I think it may be too soon to give up on the one she's on now though.
Also, I don't think you're really losing her, even though it feels that way. My guess is that the anxiety/depression are taking a lot out of her right now. It can be hard to feel close to people when you're depressed. Once she gets the right kind and right dose, that'll improve.
Try to get her out when you can. She may not want to because people with depression sometimes don't feel like doing anything. But it can be very helpful. Fresh air and sunshine can help. Maybe you can go for walks together when it's sunny.
Music also can be a good mood lifter. You can watch funny shows/movies together. Encourage her to spend time with friends (so long as they're not a bad influence,of course) Above all, reassure her you love her and be patient. My husband was very good at doing that, and even though he might not have been able to see it at the time, it did help.
I would also recommend asking her counselor to give you the names of some good books/ websites where you can read about anxiety/depression. I think it's helpful for people who live with someone who has it, to understand what they're going through. You could also ask her counselor if there are any support groups.
Again, hang in there. It will get better :)